Projeto Infnet¶

  • Algoritmos Não-Supervisionados para clusterização
  • Realizado: Patrícia Ferreira da Silva
  • Ministrado: Luiz Fernando de Frias

Objetivo¶

  • Segregar grupos com traços semelhantes e atribuí-los a clusters.

Importação das bibliotecas¶

In [3]:
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import make_pipeline
import plotly.express as px
import scipy.cluster.hierarchy as sch
import matplotlib.pyplot as plt
import numpy as np

from sklearn_extra.cluster import KMedoids
from sklearn.datasets import make_blobs
import requests 
import folium

EDA¶

In [4]:
dataset = pd.read_csv('Country.csv')
In [5]:
dataset.head(16)
Out[5]:
country child_mort exports health imports income inflation life_expec total_fer gdpp
0 Afghanistan 90.2 10.0 7.58 44.9 1610 9.440 56.2 5.82 553
1 Albania 16.6 28.0 6.55 48.6 9930 4.490 76.3 1.65 4090
2 Algeria 27.3 38.4 4.17 31.4 12900 16.100 76.5 2.89 4460
3 Angola 119.0 62.3 2.85 42.9 5900 22.400 60.1 6.16 3530
4 Antigua and Barbuda 10.3 45.5 6.03 58.9 19100 1.440 76.8 2.13 12200
5 Argentina 14.5 18.9 8.10 16.0 18700 20.900 75.8 2.37 10300
6 Armenia 18.1 20.8 4.40 45.3 6700 7.770 73.3 1.69 3220
7 Australia 4.8 19.8 8.73 20.9 41400 1.160 82.0 1.93 51900
8 Austria 4.3 51.3 11.00 47.8 43200 0.873 80.5 1.44 46900
9 Azerbaijan 39.2 54.3 5.88 20.7 16000 13.800 69.1 1.92 5840
10 Bahamas 13.8 35.0 7.89 43.7 22900 -0.393 73.8 1.86 28000
11 Bahrain 8.6 69.5 4.97 50.9 41100 7.440 76.0 2.16 20700
12 Bangladesh 49.4 16.0 3.52 21.8 2440 7.140 70.4 2.33 758
13 Barbados 14.2 39.5 7.97 48.7 15300 0.321 76.7 1.78 16000
14 Belarus 5.5 51.4 5.61 64.5 16200 15.100 70.4 1.49 6030
15 Belgium 4.5 76.4 10.70 74.7 41100 1.880 80.0 1.86 44400
  • morte infantil
  • exportações
  • saúde
  • importações
  • renda
  • inflação
  • expectativa de vida
  • oferta total
  • gdpp
In [6]:
dataset.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 167 entries, 0 to 166
Data columns (total 10 columns):
 #   Column      Non-Null Count  Dtype  
---  ------      --------------  -----  
 0   country     167 non-null    object 
 1   child_mort  167 non-null    float64
 2   exports     167 non-null    float64
 3   health      167 non-null    float64
 4   imports     167 non-null    float64
 5   income      167 non-null    int64  
 6   inflation   167 non-null    float64
 7   life_expec  167 non-null    float64
 8   total_fer   167 non-null    float64
 9   gdpp        167 non-null    int64  
dtypes: float64(7), int64(2), object(1)
memory usage: 13.2+ KB
In [7]:
dataset.describe().T
Out[7]:
count mean std min 25% 50% 75% max
child_mort 167.0 38.270060 40.328931 2.6000 8.250 19.30 62.10 208.00
exports 167.0 41.108976 27.412010 0.1090 23.800 35.00 51.35 200.00
health 167.0 6.815689 2.746837 1.8100 4.920 6.32 8.60 17.90
imports 167.0 46.890215 24.209589 0.0659 30.200 43.30 58.75 174.00
income 167.0 17144.688623 19278.067698 609.0000 3355.000 9960.00 22800.00 125000.00
inflation 167.0 7.781832 10.570704 -4.2100 1.810 5.39 10.75 104.00
life_expec 167.0 70.555689 8.893172 32.1000 65.300 73.10 76.80 82.80
total_fer 167.0 2.947964 1.513848 1.1500 1.795 2.41 3.88 7.49
gdpp 167.0 12964.155689 18328.704809 231.0000 1330.000 4660.00 14050.00 105000.00
In [8]:
# Quantidade de paises 
dataset.country.nunique(dropna = True)
Out[8]:
167
In [9]:
plt.figure(figsize=(15,5))
sns.boxplot(data=dataset,orient='h')
Out[9]:
<AxesSubplot: >
In [10]:
q1 = dataset.income.quantile(0.25)
q3 = dataset.income.quantile(0.75)
IQR = q3 - q1
lower_limit = q1 - 1.5 * IQR
upper_limit = q3 + 1.5 * IQR
k1=dataset[dataset["income"]>upper_limit]
print("outliers on right side in income is \n",k1["income"],"\n")
dataset=dataset[dataset["income"]<upper_limit]
sns.boxplot(dataset["income"])

outliers on right side in income is 
 23      80600
82      75200
91      91700
114     62300
123    125000
133     72100
145     55500
157     57600
Name: income, dtype: int64
Out[10]:
<AxesSubplot: >
In [11]:
q1 = dataset.income.quantile(0.25)
q3 = dataset.income.quantile(0.75)
IQR = q3 - q1
lower_limit = q1 - 1.5 * IQR
upper_limit = q3 + 1.5 * IQR
k1=dataset[dataset["gdpp"]>upper_limit]
print("outliers on right side in gdpp is \n",k1["gdpp"],"\n")
dataset=dataset[dataset["gdpp"]<upper_limit]
sns.boxplot(dataset["gdpp"])

outliers on right side in gdpp is 
 7      51900
8      46900
29     47400
44     58000
53     46200
73     48700
110    50300
144    52100
159    48400
Name: gdpp, dtype: int64
Out[11]:
<AxesSubplot: >
In [12]:
plt.figure(figsize=(15,5))
sns.boxplot(data=dataset,orient='h')
Out[12]:
<AxesSubplot: >
In [13]:
q1 = dataset.gdpp.quantile(0.25)
q3 = dataset.gdpp.quantile(0.75)
IQR = q3 - q1
lower_limit = q1 - 1.5 * IQR
upper_limit = q3 + 1.5 * IQR
k1=dataset[dataset["income"] > upper_limit]
data2=dataset[dataset["gdpp"] < upper_limit]
sns.boxplot(dataset["gdpp"])
Out[13]:
<AxesSubplot: >
In [14]:
plt.figure(figsize=(15,5))
sns.boxplot(data=data2,orient='h')
Out[14]:
<AxesSubplot: >
In [15]:
#tamanho do dataset
data2.shape
Out[15]:
(137, 10)
In [16]:
data2
Out[16]:
country child_mort exports health imports income inflation life_expec total_fer gdpp
0 Afghanistan 90.2 10.0 7.58 44.9 1610 9.44 56.2 5.82 553
1 Albania 16.6 28.0 6.55 48.6 9930 4.49 76.3 1.65 4090
2 Algeria 27.3 38.4 4.17 31.4 12900 16.10 76.5 2.89 4460
3 Angola 119.0 62.3 2.85 42.9 5900 22.40 60.1 6.16 3530
4 Antigua and Barbuda 10.3 45.5 6.03 58.9 19100 1.44 76.8 2.13 12200
... ... ... ... ... ... ... ... ... ... ...
162 Vanuatu 29.2 46.6 5.25 52.7 2950 2.62 63.0 3.50 2970
163 Venezuela 17.1 28.5 4.91 17.6 16500 45.90 75.4 2.47 13500
164 Vietnam 23.3 72.0 6.84 80.2 4490 12.10 73.1 1.95 1310
165 Yemen 56.3 30.0 5.18 34.4 4480 23.60 67.5 4.67 1310
166 Zambia 83.1 37.0 5.89 30.9 3280 14.00 52.0 5.40 1460

137 rows × 10 columns

Exploração dos dados¶

In [17]:
# Quantidade de paises 
data2.country.nunique(dropna = True)
#data2=data2.drop(['Cluster'],axis=1)
#occur = data2.groupby(['country']).size()
#occur
Out[17]:
137
In [18]:
pd.set_option("display.float", "{:.2f}".format)
data2.describe()
Out[18]:
child_mort exports health imports income inflation life_expec total_fer gdpp
count 137.00 137.00 137.00 137.00 137.00 137.00 137.00 137.00 137.00
mean 45.51 38.13 6.36 46.90 10257.39 8.88 68.42 3.20 5499.37
std 41.11 22.14 2.37 21.36 9371.18 11.21 8.37 1.56 5661.36
min 3.20 0.11 1.97 0.07 609.00 -4.21 32.10 1.23 231.00
25% 14.60 22.80 4.84 31.40 2660.00 2.61 62.20 1.92 1170.00
50% 28.10 32.90 5.89 44.90 7710.00 6.35 70.40 2.65 3450.00
75% 64.40 50.50 7.76 58.90 15400.00 12.10 74.70 4.56 8080.00
max 208.00 153.00 14.20 154.00 45400.00 104.00 80.40 7.49 23400.00
In [19]:
# variáveis que serão utilizadas 
p = data2.hist(figsize = (10,12))
In [20]:
fig = px.choropleth(data2,
                    locationmode='country names',
                    locations='country',
                    color='inflation',
                    title='Paises com alta inflação'
                   )
fig.show()
In [21]:
fig = px.choropleth(data2,
                    locationmode='country names',
                    locations='country',
                    color='child_mort',
                    title='Paises com indice alto por morte infantil'
                   )
fig.show()

## paises com cores mais claras, são paises com alta mortalidade infantil
In [22]:
fig = px.choropleth(data2,
                    locationmode='country names',
                    locations='country',
                    color='life_expec',
                    title='Paises com alta expectativa de vida'
                   )
fig.show()
In [23]:
fig = px.choropleth(data2,
                    locationmode='country names',
                    locations='country',
                    color='health',
                    title='Paises com Indice de saúde'
                   )
fig.show()
In [24]:
data2
Out[24]:
country child_mort exports health imports income inflation life_expec total_fer gdpp
0 Afghanistan 90.20 10.00 7.58 44.90 1610 9.44 56.20 5.82 553
1 Albania 16.60 28.00 6.55 48.60 9930 4.49 76.30 1.65 4090
2 Algeria 27.30 38.40 4.17 31.40 12900 16.10 76.50 2.89 4460
3 Angola 119.00 62.30 2.85 42.90 5900 22.40 60.10 6.16 3530
4 Antigua and Barbuda 10.30 45.50 6.03 58.90 19100 1.44 76.80 2.13 12200
... ... ... ... ... ... ... ... ... ... ...
162 Vanuatu 29.20 46.60 5.25 52.70 2950 2.62 63.00 3.50 2970
163 Venezuela 17.10 28.50 4.91 17.60 16500 45.90 75.40 2.47 13500
164 Vietnam 23.30 72.00 6.84 80.20 4490 12.10 73.10 1.95 1310
165 Yemen 56.30 30.00 5.18 34.40 4480 23.60 67.50 4.67 1310
166 Zambia 83.10 37.00 5.89 30.90 3280 14.00 52.00 5.40 1460

137 rows × 10 columns

In [25]:
data2.describe().T
Out[25]:
count mean std min 25% 50% 75% max
child_mort 137.00 45.51 41.11 3.20 14.60 28.10 64.40 208.00
exports 137.00 38.13 22.14 0.11 22.80 32.90 50.50 153.00
health 137.00 6.36 2.37 1.97 4.84 5.89 7.76 14.20
imports 137.00 46.90 21.36 0.07 31.40 44.90 58.90 154.00
income 137.00 10257.39 9371.18 609.00 2660.00 7710.00 15400.00 45400.00
inflation 137.00 8.88 11.21 -4.21 2.61 6.35 12.10 104.00
life_expec 137.00 68.42 8.37 32.10 62.20 70.40 74.70 80.40
total_fer 137.00 3.20 1.56 1.23 1.92 2.65 4.56 7.49
gdpp 137.00 5499.37 5661.36 231.00 1170.00 3450.00 8080.00 23400.00
In [26]:
# Matriz de correlação

corr_matrix = data2.corr()
fig, ax = plt.subplots(figsize=(15, 15))
ax = sns.heatmap(corr_matrix,
                 annot=True,
                 linewidths=0.5,
                 fmt=".2f",
                 cmap="YlGnBu");
bottom, top = ax.get_ylim()
ax.set_ylim(bottom + 0.5, top - 0.5)

C:\Users\BlueShift\AppData\Local\Temp\ipykernel_7816\2477129727.py:3: FutureWarning:

The default value of numeric_only in DataFrame.corr is deprecated. In a future version, it will default to False. Select only valid columns or specify the value of numeric_only to silence this warning.
Out[26]:
(9.5, -0.5)
In [ ]:

Clusterização¶

  • K-Médias
  • Pré processamento
In [65]:
x=data2.drop(['country'],axis=1).values
Out[65]:
array([[9.02e+01, 1.00e+01, 7.58e+00, ..., 5.82e+00, 5.53e+02, 1.00e+00],
       [1.66e+01, 2.80e+01, 6.55e+00, ..., 1.65e+00, 4.09e+03, 1.00e+00],
       [2.73e+01, 3.84e+01, 4.17e+00, ..., 2.89e+00, 4.46e+03, 0.00e+00],
       ...,
       [2.33e+01, 7.20e+01, 6.84e+00, ..., 1.95e+00, 1.31e+03, 1.00e+00],
       [5.63e+01, 3.00e+01, 5.18e+00, ..., 4.67e+00, 1.31e+03, 1.00e+00],
       [8.31e+01, 3.70e+01, 5.89e+00, ..., 5.40e+00, 1.46e+03, 1.00e+00]])

Normalização dos dados¶

In [28]:
#normalização
scaler = StandardScaler()
X = scaler.fit_transform(x)
x
'''
normalized_df = (x-x.mean())/x.std()
normalized_df'''
Out[28]:
'\nnormalized_df = (x-x.mean())/x.std()\nnormalized_df'
In [29]:
#Quanto maior o valor de WCSS, o agrupamento será menos preciso.
#Quanto menor o valor de WCSSS, o agrupamento será mais preciso.
#kmeans.intertia_ tem o valor WCSS para o número atual de clusters.
#init = 'K-means++' é a inicialização do centroide para cada cluster. (Escolhendo o ponto de dados aleatório certo em cada cluster.)

Wcss=[]
for i in range(1,11):
    kmeans=KMeans(n_clusters=i,init='k-means++',random_state=9)
    kmeans.fit(x)
    Wcss.append(kmeans.inertia_)
print(Wcss)

[16302714565.573353, 5271125573.8398, 2486196021.565976, 1500330532.5287132, 1008471886.0701281, 674744053.0271779, 546427395.4781845, 454192475.71572864, 400608402.4926262, 344858346.21710336]
In [30]:
# Escolha do número de cluster
sns.set()
plt.plot(range(1,11),Wcss)
plt.title('The Elbow Point Graph')
plt.xlabel('Number of Clusters')
plt.ylabel('WCSS')
plt.show()

Treinando o Modelo¶

In [31]:
kmeans=KMeans(n_clusters=3,init='k-means++',random_state=9)
y=kmeans.fit_predict(x)
y
Out[31]:
array([1, 1, 0, 1, 0, 0, 1, 0, 2, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1,
       1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 0, 1, 1, 1, 2, 1, 0,
       1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1,
       1, 0, 0, 1, 1, 2, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 1, 1, 0, 1, 1,
       1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 0, 2, 0, 0, 1, 1, 2, 1, 0, 0, 1,
       2, 2, 1, 0, 2, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1,
       1, 0, 1, 1, 1])

Visualizando os clusters¶

In [32]:
n_clusters = 3
plt.figure(figsize=(8,8))
for s in np.arange(1,2):
    kmeans=KMeans(n_clusters=3,init='k-means++',max_iter = 100, random_state=9)
    #model = KMeans(n_clusters=n_clusters, init="k-means++")
    pred = kmeans.fit_predict(X)
    plt.figure(figsize=(20,10))
    
    for i in range(0, n_clusters):
        plt.scatter(X[pred == i, 0], X[pred == i, 1], s=50, label="Cluster %d" % i)
   # plt.scatter(X[:,0],X[:,1], c=pred)
    plt.scatter(kmeans.cluster_centers_[:,0], kmeans.cluster_centers_[:,1], s = 200, c = 'black', label='centroids')
    plt.title("Clusters")
    plt.legend()
plt.show()

<Figure size 800x800 with 0 Axes>
In [73]:
import numpy as np

O país, de acordo com o algoritmo, melhor representa o seu agrupamento¶

In [69]:
k_fit = kmeans.fit(x)
In [70]:
## Qual pais esta perto do cluster 
k_fit.transform(x)
Out[70]:
array([[16796.11746056,  3054.0401433 , 36657.22186935],
       [ 7898.09997051,  5999.0303086 , 27733.28970699],
       [ 5545.37763952,  8933.88921504, 25091.42672774],
       [11600.87854944,  2232.25889556, 31448.34063079],
       [ 4385.87266998, 17982.25783918, 15695.37947381],
       [ 2879.98521118, 16623.92306551, 16994.73080394],
       [11056.79501624,  2693.19143891, 30922.64343941],
       [ 3111.81173158, 12305.16132595, 21793.96204877],
       [27572.47927536, 41278.63324167,  8177.2317867 ],
       [15976.39754809,  2230.75735718, 35841.19914027],
       [ 7104.34318068, 17829.20895297, 18051.84270192],
       [ 2918.03835485, 12555.62849826, 21519.06767322],
       [ 9473.6230537 ,  4283.87250397, 29332.19903691],
       [16512.01192901,  2775.18827098, 36371.68002449],
       [11858.46422775,  2106.42985638, 31715.52835312],
       [12808.59089586,  1084.03378649, 32673.74893475],
       [ 7762.62195935,  6014.85431476, 27625.4905621 ],
       [ 3862.01091879,  9994.99512784, 23675.68821066],
       [ 2796.98897084, 13751.47288807, 20274.77637683],
       [ 2275.4683255 , 12014.58835712, 21749.9721985 ],
       [16941.49565514,  3206.04080577, 36800.32767813],
       [17690.40080004,  3954.96677989, 37548.46723816],
       [15893.32476707,  2148.26237692, 35758.28298557],
       [15508.97136055,  1785.28633913, 35367.43972335],
       [11766.18012758,  2029.10641389, 31620.32827936],
       [17477.36008947,  3753.47027208, 37332.24027003],
       [16347.95000513,  2618.4007964 , 36206.03469335],
       [ 5112.21081324, 18632.19587597, 15113.5360167 ],
       [ 7948.41894668,  5822.44698148, 27812.68736424],
       [ 5909.42137708,  7856.23712604, 25760.02374645],
       [16863.8048185 ,  3146.04591263, 36718.3182455 ],
       [17775.37983196,  4053.23542957, 37629.26464896],
       [12602.67833734,  1173.0470071 , 32462.07911114],
       [ 3244.97056254, 10692.02842001, 22965.07214735],
       [15527.45681527,  1791.9963858 , 35387.95156837],
       [ 6022.19483038, 19551.32247998, 14224.54985466],
       [16285.35216191, 29890.23114661,  4730.84441785],
       [ 6149.28625526,  7625.236536  , 26010.33096045],
       [ 8045.36145795,  5708.88862231, 27911.71937405],
       [ 8941.65979014,  5571.75219244, 28642.29116708],
       [10674.78122089,  3150.99826458, 30536.99825627],
       [19344.44561387, 33051.26205858,  2453.22001199],
       [16996.10864938,  3255.57004834, 36856.61342987],
       [ 8646.03381289, 22308.35436853, 11403.14789867],
       [10278.11192963,  3469.93566172, 30143.64879677],
       [  785.01464332, 12995.7508363 , 20615.33263287],
       [16748.25285358,  3005.34493742, 36609.70402022],
       [11168.33625949,  2608.20460784, 31034.49496861],
       [15161.94318135,  1418.27268662, 35024.60048772],
       [ 5202.62888417,  8754.72282731, 24941.36511515],
       [11255.376368  ,  2541.52687316, 31120.71471939],
       [17114.96838149,  3395.66689021, 36969.31185823],
       [16990.10081327,  3254.15625925, 36849.02538421],
       [11889.27641359,  1866.8645788 , 31750.46609673],
       [16838.53869032,  3109.05048522, 36696.00603119],
       [ 7414.42481632, 21152.2631136 , 12460.34578051],
       [13990.45735479,   603.93644026, 33855.69179677],
       [ 9684.78866161,  4264.89719909, 29525.02007349],
       [ 2718.3664292 , 13853.18001769, 20272.52774004],
       [ 5633.56810959,  8753.67710994, 25228.34043543],
       [ 9206.49284519,  4578.23609935, 29055.09046745],
       [ 8513.08808267,  5427.41108128, 28343.49539006],
       [ 3944.33440735, 17306.79415153, 16574.68146126],
       [15835.72984753,  2091.07081299, 35698.39372086],
       [16241.20226735,  2637.04616061, 36078.81927587],
       [15613.49680222,  1872.01896138, 35478.97582259],
       [14465.72683481,   879.20782288, 34331.38319782],
       [ 3181.80008544, 16814.30337128, 16826.22891077],
       [  168.47876931, 13825.40750109, 19792.50676712],
       [15821.6544647 ,  2097.48438971, 35679.58875751],
       [17699.18746088,  3972.78157181, 37554.45333543],
       [13807.08741737, 27236.19921657,  8110.10014098],
       [ 5809.06727307, 19554.93613418, 14057.50851597],
       [ 6485.54618265,  7533.54253175, 26263.86280203],
       [17056.51806722,  3313.58691639, 36917.84079834],
       [17346.69426043,  3617.43269079, 37203.27072101],
       [ 4944.1610687 , 18222.96205366, 15807.66656454],
       [ 5951.802814  ,  8041.1547024 , 25684.69248761],
       [16493.70711932,  2752.84852737, 36354.6382527 ],
       [17179.68904281, 30684.78960205,  4998.4433097 ],
       [14994.56200877,  1254.8021057 , 34859.96867229],
       [  982.21083205, 13060.38477621, 20597.06764004],
       [14189.8833536 ,  1344.48350902, 34002.59889511],
       [14267.19685527,   527.18181596, 34132.12628247],
       [10536.771697  ,  3455.77785129, 30379.2455573 ],
       [ 3130.16543536, 10768.94770343, 22910.29324751],
       [11482.9358138 ,  2290.2767644 , 31349.27988676],
       [17463.98552108,  3736.03992427, 37320.00604073],
       [14766.72266451,  1136.82485617, 34632.46589699],
       [ 8565.92058627,  5253.25910338, 28400.4203603 ],
       [16448.10013461,  2701.70021657, 36311.82967586],
       [17589.54022731,  3860.33384029, 37445.73894948],
       [12844.60279459,   915.49175552, 32709.50504255],
       [30926.53853757, 44496.2300869 , 12282.81133101],
       [14269.39008234,   910.01548938, 34131.93882209],
       [ 1152.6358325 , 12658.06603423, 20970.95523217],
       [10551.11585854,  3229.15373079, 30416.69915559],
       [ 7337.39887385,  6416.77961962, 27203.65875018],
       [12567.56325917,  1286.70770847, 32432.98787725],
       [ 6721.35044285, 20464.34355782, 13146.62833769],
       [17481.46908642, 30750.36857278,  6567.22826625],
       [ 1792.37671005, 14866.02841549, 18909.93004889],
       [ 7160.19666847, 20713.3155156 , 13229.35434049],
       [17016.782534  ,  3283.1505121 , 36875.07147524],
       [12080.99753784,  1846.81619871, 31920.38951667],
       [31020.78228566, 44588.31726261, 12382.83514272],
       [16079.22266979,  2346.65266171, 35938.40316731],
       [ 4946.72877976,  9061.02978937, 24699.7867312 ],
       [ 4629.87075867, 18350.01451882, 15301.06624888],
       [17211.41842968,  3472.78992672, 37071.04866205],
       [11845.92239773, 25502.71273485,  8323.03380713],
       [19135.9268088 , 32469.37724591,  5849.24334536],
       [16289.7709484 ,  2630.81725764, 36135.52150393],
       [ 4479.83961028,  9344.12000764, 24289.67234302],
       [19386.3566541 , 32953.49278722,  3722.11969912],
       [ 9767.05737341,  4320.61110165, 29584.58329628],
       [ 6803.95460551,  7044.4555924 , 26616.09600324],
       [14808.56478073,  1065.52419213, 34671.4174841 ],
       [ 2062.00250072, 11740.3026955 , 21875.75716901],
       [16270.70097147,  2525.45329597, 36133.49080487],
       [16306.20065958,  2560.34530128, 36169.28707421],
       [ 4692.78265987,  9693.50991964, 24240.19443821],
       [15274.47026889,  2977.47506582, 34968.99123521],
       [17175.62683791,  3441.78438107, 37033.72604727],
       [12412.68334773,  1731.06642752, 32235.0374336 ],
       [ 7500.90325826,  6457.04898502, 27315.15871658],
       [ 2542.86645891, 16234.62273343, 17383.65916067],
       [ 7679.87649516,  6141.85427752, 27532.55247421],
       [16835.86452967,  3097.84378198, 36695.59512251],
       [10259.0424303 ,  3640.19562812, 30111.28265909],
       [ 3099.25856516, 16192.80900234, 17619.95815404],
       [14117.34328139,   575.30935928, 33983.46606883],
       [14497.36045572,  1715.14514926, 34290.47636648],
       [ 4565.51148999, 16782.34688097, 17558.81607933],
       [13945.20101898,   661.7743349 , 33809.49770229],
       [13953.57010393,   656.2380199 , 33817.9910999 ],
       [14896.39389145,  1155.14969948, 34758.74091593]])
In [76]:
np.min(k_fit.transform(x), axis=1)
Out[76]:
array([ 3054.0401433 ,  5999.0303086 ,  5545.37763952,  2232.25889556,
        4385.87266998,  2879.98521118,  2693.19143891,  3111.81173158,
        8177.2317867 ,  2230.75735718,  7104.34318068,  2918.03835485,
        4283.87250397,  2775.18827098,  2106.42985638,  1084.03378649,
        6014.85431476,  3862.01091879,  2796.98897084,  2275.4683255 ,
        3206.04080577,  3954.96677989,  2148.26237692,  1785.28633913,
        2029.10641389,  3753.47027208,  2618.4007964 ,  5112.21081324,
        5822.44698148,  5909.42137708,  3146.04591263,  4053.23542957,
        1173.0470071 ,  3244.97056254,  1791.9963858 ,  6022.19483038,
        4730.84441785,  6149.28625526,  5708.88862231,  5571.75219244,
        3150.99826458,  2453.22001199,  3255.57004834,  8646.03381289,
        3469.93566172,   785.01464332,  3005.34493742,  2608.20460784,
        1418.27268662,  5202.62888417,  2541.52687316,  3395.66689021,
        3254.15625925,  1866.8645788 ,  3109.05048522,  7414.42481632,
         603.93644026,  4264.89719909,  2718.3664292 ,  5633.56810959,
        4578.23609935,  5427.41108128,  3944.33440735,  2091.07081299,
        2637.04616061,  1872.01896138,   879.20782288,  3181.80008544,
         168.47876931,  2097.48438971,  3972.78157181,  8110.10014098,
        5809.06727307,  6485.54618265,  3313.58691639,  3617.43269079,
        4944.1610687 ,  5951.802814  ,  2752.84852737,  4998.4433097 ,
        1254.8021057 ,   982.21083205,  1344.48350902,   527.18181596,
        3455.77785129,  3130.16543536,  2290.2767644 ,  3736.03992427,
        1136.82485617,  5253.25910338,  2701.70021657,  3860.33384029,
         915.49175552, 12282.81133101,   910.01548938,  1152.6358325 ,
        3229.15373079,  6416.77961962,  1286.70770847,  6721.35044285,
        6567.22826625,  1792.37671005,  7160.19666847,  3283.1505121 ,
        1846.81619871, 12382.83514272,  2346.65266171,  4946.72877976,
        4629.87075867,  3472.78992672,  8323.03380713,  5849.24334536,
        2630.81725764,  4479.83961028,  3722.11969912,  4320.61110165,
        6803.95460551,  1065.52419213,  2062.00250072,  2525.45329597,
        2560.34530128,  4692.78265987,  2977.47506582,  3441.78438107,
        1731.06642752,  6457.04898502,  2542.86645891,  6141.85427752,
        3097.84378198,  3640.19562812,  3099.25856516,   575.30935928,
        1715.14514926,  4565.51148999,   661.7743349 ,   656.2380199 ,
        1155.14969948])
In [77]:
np.min(k_fit.transform(x), axis=1).sum()
Out[77]:
501604.0977535491

De acordo com a distancia de cada um para para seu cluster¶

  • o indice 0 é o país mais proximo do cluster 1
  • o indice 1 é o mais proximo do cluster 0
  • o indice 8 é o país mais proximo do cluster 2
In [81]:
mag_df= pd.DataFrame(
zip(
    np.min(k_fit.transform(x),axis=1),
    k_fit.labels_
  ), columns=['distancia', 'cluster']
)
mag_df.head(20)
Out[81]:
distancia cluster
0 3054.04 1
1 5999.03 1
2 5545.38 0
3 2232.26 1
4 4385.87 0
5 2879.99 0
6 2693.19 1
7 3111.81 0
8 8177.23 2
9 2230.76 1
10 7104.34 0
11 2918.04 0
12 4283.87 1
13 2775.19 1
14 2106.43 1
15 1084.03 1
16 6014.85 1
17 3862.01 0
18 2796.99 0
19 2275.47 0
In [86]:
data2.head(10)
Out[86]:
country child_mort exports health imports income inflation life_expec total_fer gdpp Cluster
0 Afghanistan 90.20 10.00 7.58 44.90 1610 9.44 56.20 5.82 553 1
1 Albania 16.60 28.00 6.55 48.60 9930 4.49 76.30 1.65 4090 1
2 Algeria 27.30 38.40 4.17 31.40 12900 16.10 76.50 2.89 4460 0
3 Angola 119.00 62.30 2.85 42.90 5900 22.40 60.10 6.16 3530 1
4 Antigua and Barbuda 10.30 45.50 6.03 58.90 19100 1.44 76.80 2.13 12200 0
5 Argentina 14.50 18.90 8.10 16.00 18700 20.90 75.80 2.37 10300 0
6 Armenia 18.10 20.80 4.40 45.30 6700 7.77 73.30 1.69 3220 1
9 Azerbaijan 39.20 54.30 5.88 20.70 16000 13.80 69.10 1.92 5840 0
11 Bahrain 8.60 69.50 4.97 50.90 41100 7.44 76.00 2.16 20700 2
12 Bangladesh 49.40 16.00 3.52 21.80 2440 7.14 70.40 2.33 758 1
In [33]:
data2['Cluster']=y
data2

C:\Users\BlueShift\AppData\Local\Temp\ipykernel_7816\498247848.py:1: SettingWithCopyWarning:


A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
Out[33]:
country child_mort exports health imports income inflation life_expec total_fer gdpp Cluster
0 Afghanistan 90.20 10.00 7.58 44.90 1610 9.44 56.20 5.82 553 1
1 Albania 16.60 28.00 6.55 48.60 9930 4.49 76.30 1.65 4090 1
2 Algeria 27.30 38.40 4.17 31.40 12900 16.10 76.50 2.89 4460 0
3 Angola 119.00 62.30 2.85 42.90 5900 22.40 60.10 6.16 3530 1
4 Antigua and Barbuda 10.30 45.50 6.03 58.90 19100 1.44 76.80 2.13 12200 0
... ... ... ... ... ... ... ... ... ... ... ...
162 Vanuatu 29.20 46.60 5.25 52.70 2950 2.62 63.00 3.50 2970 1
163 Venezuela 17.10 28.50 4.91 17.60 16500 45.90 75.40 2.47 13500 0
164 Vietnam 23.30 72.00 6.84 80.20 4490 12.10 73.10 1.95 1310 1
165 Yemen 56.30 30.00 5.18 34.40 4480 23.60 67.50 4.67 1310 1
166 Zambia 83.10 37.00 5.89 30.90 3280 14.00 52.00 5.40 1460 1

137 rows × 11 columns

Agrupando os 3 grupos de clusters¶

In [34]:
### Clusters 0,1 e 2
df_0=data2[data2['Cluster']==0]
df_1=data2[data2['Cluster']==1]
df_2=data2[data2['Cluster']==2]
In [35]:
#Países que representa seus clusters
import plotly.express as px
fig  = px.scatter(data2, x = 'Cluster', y = 'country')

fig.show()
In [36]:
#Cluster 2
df_2
Out[36]:
country child_mort exports health imports income inflation life_expec total_fer gdpp Cluster
11 Bahrain 8.60 69.50 4.97 50.90 41100 7.44 76.00 2.16 20700 2
43 Czech Republic 3.40 66.00 7.88 62.90 28300 -1.43 77.50 1.51 19800 2
49 Equatorial Guinea 111.00 85.80 4.48 58.90 33700 24.90 60.90 5.21 17100 2
89 Libya 16.60 65.60 3.88 42.10 29600 14.20 76.10 2.41 12100 2
98 Malta 6.80 153.00 8.65 154.00 28300 3.83 80.30 1.36 21100 2
115 Oman 11.70 65.70 2.77 41.20 45300 15.60 76.10 2.90 19300 2
122 Portugal 3.90 29.90 11.00 37.40 27200 0.64 79.80 1.39 22500 2
128 Saudi Arabia 15.70 49.60 4.29 33.00 45400 17.20 75.10 2.96 19300 2
134 Slovak Republic 7.00 76.30 8.79 77.80 25200 0.48 75.50 1.43 16600 2
135 Slovenia 3.20 64.30 9.41 62.90 28700 -0.99 79.50 1.57 23400 2
138 South Korea 4.10 49.40 6.93 46.20 30400 3.16 80.10 1.23 22100 2
In [37]:
#Cluster 1
df_1
Out[37]:
country child_mort exports health imports income inflation life_expec total_fer gdpp Cluster
0 Afghanistan 90.20 10.00 7.58 44.90 1610 9.44 56.20 5.82 553 1
1 Albania 16.60 28.00 6.55 48.60 9930 4.49 76.30 1.65 4090 1
3 Angola 119.00 62.30 2.85 42.90 5900 22.40 60.10 6.16 3530 1
6 Armenia 18.10 20.80 4.40 45.30 6700 7.77 73.30 1.69 3220 1
12 Bangladesh 49.40 16.00 3.52 21.80 2440 7.14 70.40 2.33 758 1
... ... ... ... ... ... ... ... ... ... ... ...
161 Uzbekistan 36.30 31.70 5.81 28.50 4240 16.50 68.80 2.34 1380 1
162 Vanuatu 29.20 46.60 5.25 52.70 2950 2.62 63.00 3.50 2970 1
164 Vietnam 23.30 72.00 6.84 80.20 4490 12.10 73.10 1.95 1310 1
165 Yemen 56.30 30.00 5.18 34.40 4480 23.60 67.50 4.67 1310 1
166 Zambia 83.10 37.00 5.89 30.90 3280 14.00 52.00 5.40 1460 1

84 rows × 11 columns

In [38]:
#Cluster 0
df_0
Out[38]:
country child_mort exports health imports income inflation life_expec total_fer gdpp Cluster
2 Algeria 27.30 38.40 4.17 31.40 12900 16.10 76.50 2.89 4460 0
4 Antigua and Barbuda 10.30 45.50 6.03 58.90 19100 1.44 76.80 2.13 12200 0
5 Argentina 14.50 18.90 8.10 16.00 18700 20.90 75.80 2.37 10300 0
9 Azerbaijan 39.20 54.30 5.88 20.70 16000 13.80 69.10 1.92 5840 0
13 Barbados 14.20 39.50 7.97 48.70 15300 0.32 76.70 1.78 16000 0
14 Belarus 5.50 51.40 5.61 64.50 16200 15.10 70.40 1.49 6030 0
21 Botswana 52.50 43.60 8.30 51.30 13300 8.92 57.10 2.88 6350 0
22 Brazil 19.80 10.70 9.01 11.80 14500 8.41 74.20 1.80 11200 0
24 Bulgaria 10.80 50.20 6.87 53.00 15300 1.11 73.90 1.57 6840 0
33 Chile 8.70 37.70 7.96 31.30 19400 8.96 79.10 1.88 12900 0
35 Colombia 18.60 15.90 7.59 17.80 10900 3.86 76.40 2.01 6250 0
39 Costa Rica 10.20 33.20 10.90 35.00 13000 6.57 80.40 1.92 8200 0
41 Croatia 5.50 37.60 7.76 38.10 20100 0.82 76.30 1.55 13500 0
45 Dominican Republic 34.40 22.70 6.22 33.30 11100 5.44 74.60 2.60 5450 0
51 Estonia 4.50 75.10 6.03 68.70 22700 1.74 76.00 1.72 14600 0
55 Gabon 63.70 57.70 3.50 18.90 15400 16.60 62.90 4.08 8750 0
61 Grenada 14.60 23.80 5.86 49.20 11200 0.48 71.30 2.24 7370 0
67 Hungary 6.00 81.80 7.33 76.50 22300 2.33 74.50 1.25 13100 0
71 Iran 19.30 24.40 5.60 19.40 17400 15.90 74.50 1.76 6530 0
72 Iraq 36.90 39.40 8.41 34.10 12700 16.60 67.20 4.56 4500 0
79 Kazakhstan 21.50 44.20 4.29 29.90 20100 19.50 68.40 2.60 9070 0
85 Latvia 7.80 53.70 6.68 55.10 18300 -0.81 73.10 1.36 11300 0
86 Lebanon 10.30 35.80 7.03 60.20 16300 0.24 79.80 1.61 8860 0
90 Lithuania 6.10 65.30 7.04 67.20 21100 2.38 73.20 1.50 12000 0
92 Macedonia, FYR 10.40 39.80 7.09 58.10 11400 2.04 74.00 1.47 4540 0
95 Malaysia 7.90 86.90 4.39 71.00 21100 7.27 74.50 2.15 9070 0
96 Maldives 13.20 77.60 6.33 65.40 10500 2.88 77.90 2.23 7100 0
100 Mauritius 15.00 51.20 6.00 62.20 15900 1.13 73.40 1.57 8000 0
104 Montenegro 6.80 37.00 9.11 62.70 14000 1.60 76.40 1.77 6680 0
117 Panama 19.70 70.00 8.10 78.20 15400 2.59 77.80 2.62 8080 0
121 Poland 6.00 40.10 7.46 42.10 21800 1.66 76.30 1.41 12600 0
124 Romania 11.50 32.60 5.58 38.80 17800 3.53 73.70 1.59 8230 0
125 Russia 10.00 29.20 5.08 21.10 23100 14.20 69.20 1.57 10700 0
130 Serbia 7.60 32.90 10.40 47.90 12700 5.88 74.70 1.40 5410 0
131 Seychelles 14.40 93.80 3.40 108.00 20400 -4.21 73.40 2.17 10800 0
137 South Africa 53.70 28.60 8.94 27.40 12000 6.35 54.30 2.59 7280 0
141 St. Vincent and the Grenadines 20.70 26.90 4.47 57.10 9920 4.44 71.60 2.07 6230 0
143 Suriname 24.10 52.50 7.01 38.40 14200 7.20 70.30 2.52 8300 0
148 Thailand 14.90 66.50 3.88 60.80 13500 4.08 76.60 1.55 5080 0
153 Turkey 19.10 20.40 6.74 25.50 18000 7.01 78.20 2.15 10700 0
160 Uruguay 10.60 26.30 8.35 25.40 17100 4.91 76.40 2.08 11900 0
163 Venezuela 17.10 28.50 4.91 17.60 16500 45.90 75.40 2.47 13500 0

Visualizando no mapa o agrupamento dos clusters¶

In [39]:
fig = px.choropleth(data2,
                    locationmode='country names',
                    locations='country',
                    color='Cluster',
                    
                    title='Agrupamento dos Cluster',
                    
                    
                   )
fig.show()

Interpretando cada um dos Clusters¶

In [40]:
data2.groupby('Cluster').mean()

C:\Users\BlueShift\AppData\Local\Temp\ipykernel_7816\1341286259.py:1: FutureWarning:

The default value of numeric_only in DataFrameGroupBy.mean is deprecated. In a future version, numeric_only will default to False. Either specify numeric_only or select only columns which should be valid for the function.
Out[40]:
child_mort exports health imports income inflation life_expec total_fer gdpp
Cluster
0 17.74 43.85 6.70 45.21 16157.62 7.27 73.39 2.07 8947.62
1 63.06 31.04 6.15 45.94 4326.70 9.84 64.93 3.89 1947.79
2 17.45 70.46 6.64 60.66 33018.18 7.73 76.08 2.19 19454.55
De acordo com a media dos clusteres , o grupo 0 tem baixa oferta total¶
o grupo 1 tem um bom GDP - valor de bens e serviços produzidos pela economia do país menos o valor dos bens e serviços usados na produção¶
O grupo 2 tem um bom indece de renda a media dos outros campos está relativamente melhor do que os outros 2 grupos¶

Abaixo segue algumas ánalises de acordo com o clusters e algum índece de similaridade¶

Cluster 2¶

In [41]:
fig = px.choropleth(df_2,
                    locationmode='country names',
                    locations='country',
                    color='Cluster',
                    
                    title='Cluster 2',
                    
                    
                   )
fig.show()


##  Agrupamento do cluster 2, são os países com alto indice de Renda
fig = px.choropleth(data2,
                    locationmode='country names',
                    locations='country',
                    color='income',
                    
                    title='Indice de Renda para cluster 2 '
                    
                    
                   )
fig.show()

Cluster 1¶

In [42]:
#Agrupamento do cluster 1, Indice de gdpp
fig = px.choropleth(df_1,
                    locationmode='country names',
                    locations='country',
                    color='Cluster',
                    
                    title='Cluster 1',
                    
                    
                   )
fig.show()

fig = px.choropleth(data2,
                    locationmode='country names',
                    locations='country',
                    color='gdpp',
                    
                    title='Indice de gdp para cluster 1  '
                    
                    
                   )
fig.show()
#GDP
#valor de bens e serviços produzidos pela economia do país menos o valor dos bens e serviços usados na produção

Cluster 0¶

In [43]:
#Agrupamento do cluster 0, Indice de gdpp
fig = px.choropleth(df_0,
                    locationmode='country names',
                    locations='country',
                    color='Cluster',
                    
                    title='Cluster 0',
                    
                    
                   )
fig.show()

fig = px.choropleth(data2,
                    locationmode='country names',
                    locations='country',
                    color='child_mort',
                    
                    title='Indice de morte infantil para cluster 0 '
                    
                    
                   )
fig.show()

Distribuição das dimensões em cada grupo¶

Cluster 0¶

In [44]:
pd.set_option("display.float", "{:.2f}".format)
df_0.describe()
Out[44]:
child_mort exports health imports income inflation life_expec total_fer gdpp Cluster
count 42.00 42.00 42.00 42.00 42.00 42.00 42.00 42.00 42.00 42.00
mean 17.74 43.85 6.70 45.21 16157.62 7.27 73.39 2.07 8947.62 0.00
std 13.77 20.00 1.78 21.26 3694.73 8.66 5.32 0.67 3068.03 0.00
min 4.50 10.70 3.40 11.80 9920.00 -4.21 54.30 1.25 4460.00 0.00
25% 9.02 28.75 5.60 28.02 13075.00 1.68 71.97 1.57 6395.00 0.00
50% 14.30 39.45 6.80 45.00 15950.00 4.68 74.50 1.92 8265.00 0.00
75% 19.77 53.40 7.97 60.65 19000.00 8.95 76.40 2.34 11275.00 0.00
max 63.70 93.80 10.90 108.00 23100.00 45.90 80.40 4.56 16000.00 0.00
In [45]:
p = df_0.hist(figsize = (10,12))

Custer 1¶

In [46]:
pd.set_option("display.float", "{:.2f}".format)
df_1.describe()
Out[46]:
child_mort exports health imports income inflation life_expec total_fer gdpp Cluster
count 84.00 84.00 84.00 84.00 84.00 84.00 84.00 84.00 84.00 84.00
mean 63.06 31.04 6.15 45.94 4326.70 9.84 64.93 3.89 1947.79 1.00
std 41.84 16.82 2.57 18.98 2949.02 12.53 8.04 1.52 1421.81 0.00
min 6.90 0.11 1.97 0.07 609.00 0.51 32.10 1.27 231.00 1.00
25% 26.40 19.50 4.73 32.02 1767.50 3.77 59.45 2.63 706.50 1.00
50% 57.55 27.85 5.34 44.00 3355.00 6.99 65.70 3.63 1330.00 1.00
75% 90.35 41.12 6.91 56.85 6702.50 12.10 71.15 5.13 3002.50 1.00
max 208.00 85.10 14.20 101.00 10400.00 104.00 77.90 7.49 5190.00 1.00
In [47]:
p = df_1.hist(figsize = (10,12))

Custer 2¶

In [48]:
pd.set_option("display.float", "{:.2f}".format)
df_2.describe()
Out[48]:
child_mort exports health imports income inflation life_expec total_fer gdpp Cluster
count 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00
mean 17.45 70.46 6.64 60.66 33018.18 7.73 76.08 2.19 19454.55 2.00
std 31.39 31.16 2.69 33.69 7393.35 8.87 5.42 1.18 3225.64 0.00
min 3.20 29.90 2.77 33.00 25200.00 -1.43 60.90 1.23 12100.00 2.00
25% 4.00 56.95 4.38 41.65 28300.00 0.56 75.75 1.41 18200.00 2.00
50% 7.00 65.70 6.93 50.90 29600.00 3.83 76.10 1.57 19800.00 2.00
75% 13.70 72.90 8.72 62.90 37400.00 14.90 79.65 2.66 21600.00 2.00
max 111.00 153.00 11.00 154.00 45400.00 24.90 80.30 5.21 23400.00 2.00
In [49]:
p = df_2.hist(figsize = (10,12))

Clusterização Hierárquica¶

In [50]:
df = data2.set_index('country')
In [51]:
normalizedd_df = (df-df.mean())/df.std()
normalizedd_df
Out[51]:
child_mort exports health imports income inflation life_expec total_fer gdpp Cluster
country
Afghanistan 1.09 -1.27 0.52 -0.09 -0.92 0.05 -1.46 1.69 -0.87 0.39
Albania -0.70 -0.46 0.08 0.08 -0.03 -0.39 0.94 -0.99 -0.25 0.39
Algeria -0.44 0.01 -0.92 -0.73 0.28 0.64 0.97 -0.20 -0.18 -1.33
Angola 1.79 1.09 -1.48 -0.19 -0.46 1.21 -0.99 1.90 -0.35 0.39
Antigua and Barbuda -0.86 0.33 -0.14 0.56 0.94 -0.66 1.00 -0.69 1.18 -1.33
... ... ... ... ... ... ... ... ... ... ...
Vanuatu -0.40 0.38 -0.47 0.27 -0.78 -0.56 -0.65 0.19 -0.45 0.39
Venezuela -0.69 -0.43 -0.61 -1.37 0.67 3.30 0.83 -0.47 1.41 -1.33
Vietnam -0.54 1.53 0.20 1.56 -0.62 0.29 0.56 -0.80 -0.74 0.39
Yemen 0.26 -0.37 -0.50 -0.59 -0.62 1.31 -0.11 0.95 -0.74 0.39
Zambia 0.91 -0.05 -0.20 -0.75 -0.74 0.46 -1.96 1.42 -0.71 0.39

137 rows × 10 columns

In [52]:
plt.figure(figsize=(14, 5))
plt.grid(False)
dendrogram = sch.dendrogram(sch.linkage(df, method='ward'), labels=df.index)
plt.title('Dendrogram')
plt.ylabel('Euclidean Distance')
Out[52]:
Text(0, 0.5, 'Euclidean Distance')
  • A decisão do número de clusters que melhor representem diferentes grupos podem ser escolhidos observando-se o dendrograma. A melhor escolha do número de clusters é o número de linhas verticais no dendrograma cortadas por uma linha horizontal que pode atravessar verticalmente a distância máxima sem intersectar um cluster,passando uma linha na altura do 60000 pode gerar 3 grandes grupos distintos separados pelo indice.

Comparação entre clusterização hierarquica e Kmeas¶

In [53]:
fig = px.choropleth(data2,
                    locationmode='country names',
                    locations='country',
                    color='Cluster',
                    
                    title='Agrupamento dos Cluster Kmeas',
                    
                    
                   )
fig.show()

.

o kmeas foi agrupado pelos paises e similaride entre eles sendo necessario a definição do K e clusterização hierarquica pelo index e utiliza uma medida de quão próximo um registro está do outro e uma media de quão próximo o cluster está do outro.¶

Algoritmo de K-médias até sua convergência.¶

O agrupamento k-means, os dados são separados em k clusters, geralmente têm que está em forma de vetores númericos. O algoritmo calcula a média de um conjunto de pontos de dados e a distância euclidiana entre eles.

  • Precisa definir um ‘K’, ou seja, um número de clusters (ou agrupamentos).
  • Associar os centróides para cada cluster

  • Associar cada objeto de dados a seu centróide mais próximo

    O agrupamento inicial é feito atrirbuindo cada dado, objeto ao centróide que está tão próximo a ele e a primeira iteração é concluida. O algoritmo funciona em iteraçoes até que os objetos não mudem seus centros de cluster. Os centróides movem suas posições até que os critérios de convergência sejam alcançados.

Refaça o algoritmo apresentado na questão 1 a fim de garantir que o cluster seja representado pelo dado mais próximo ao seu baricentro em todas as iterações do algoritmo.¶

In [54]:
KMobj = KMedoids(n_clusters=3).fit(df)
labels = KMobj.labels_
unq_lab = set(labels)
colors_plot = [
 plt.cm.Spectral(each) for each in np.linspace(0, 1, len(unq_lab))
]

for k, col in zip(unq_lab, colors_plot):
    class_member_mask = labels == k
    xy = df[class_member_mask].values
    plt.plot(
     xy[:, 0],
     xy[:, 1],
     'o',
     markerfacecolor=tuple(col),
     markeredgecolor='white',
     markersize=10,
     );
    plt.plot(
     KMobj.cluster_centers_[:, 0],
     KMobj.cluster_centers_[:, 1],
     'o',
     markerfacecolor='orange',
     markeredgecolor='k',
     markersize=10,
    );
    plt.title('Agrupamento de KMedoids  - Medoids são representados em Laranja.', fontsize=14);
In [ ]:

O algoritmo de K-médias é sensível a outliers nos dados. Explique.¶

  • Por que os outliers influencia no resultado da média

Por que o algoritmo de DBScan é mais robusto à presença de outliers?¶

  • O DBSCAN encontra clusters baseado na densidade de observações em determinada região, ou seja, quanto maior o aglomerado de observação juntas, mais provável que elas façam parte de um mesmo subgrupo. Dessa forma, todas as observações que estão separadas das demais podem ser consideradas Outliers.
In [ ]: